1. Both support the Constitution of the United States.
2. Both support the Capitalist system.
3. Both are funded by large corporations.
Before I say anything about the differences, let me say something about these three similarities. 1. About the Constitution. Let me just say that the Swiss Constitution is better for the following reasons. First, I think it is a grave error to give such great powers to a single individual, as is given to a President or to a Prime Minister. Such persons almost invariable will work for their own benefit, their families, and their friends. As an example, just think of the activities of President Donald Trump. A single individual is also subject to bribes and threats.
A better Constitution — such as that of Switzerland — places the executive function in the hands of a council of seven individuals.
Second, the U.S. Constitution promotes Macro Democracy at all levels of government. Million vote for the President, millions vote for Senators and Representatives, millions vote for Governors, and thousands or millions vote for Mayors.
By contrast, I advocate Micro Democracy which is favored by anarchists.
2. About Capitalism. By Capitalism, I understand a political system which bars people from a free access to subsistence land. And by contrast, I view Socialism as a political system which grants people a free access to subsistence land. [I know that others view the matter differently. But when you think about it axiomatically (i.e., in terms of fundamental principles), this is the difference.]
3. As to funding. Macro Democracy requires a great amount of money for advertisement. And those with the greatest wealth (i.e., corporation) are able to contribute the most. And statistically, the candidates with the largest campaign funds tend to prevail. So both parties seek and accept corporate donations.
My stance here is to favor Micro Democracy in which funds would be useless.
Now to the differences. In reality, they are superficial and contrived. For example, there is a great fuss about voting rights. But what does it matter whether you elect a Republican Tweedle-Dee or a Democratic Tweedle-Dum.